Social dynamics and the quantifying of social forces

SOCIAL AND INDUSTRIAL EVOLUTIONARY PROCESSES ARE CONSIDERED TO BE A SEQUENCE OF REPLACEMENTS OR SUBSTITUTIONS: new ideas for old, new labor patterns for old, new technologies for old. The logistic equation has often been used to describe population growth processes and replacement processes. It sometimes suffers from contradicting observational data. It is shown here that the deviations are often associated with unusual intermittent events-wars, strikes, economic panics, etc.-and that in many cases a few years after the event it can be abstracted as an instantaneous delta function impulse. After the event, the evolutionary process continues along its normal course. A formula is derived to use the observational data to determine the strength of the impulse modeling an event.